The typical countable algebra

zbMATH Open1145.08004arXiv0801.1212MaRDI QIDQ3512578

Martin Goldstern

Publication date: 21 July 2008

Abstract: We argue that it makes sense to talk about ``typical properties of lattices, and then show that there is, up to isomorphism, a unique countable lattice L* (the Fraisse limit of the class of finite lattices) that has all ``typical properties. Among these properties are: L* is simple and locally finite, every order preserving function can be interpolated by a lattice polynomial, and every finite lattice or countable locally finite lattice embeds into L*. The same arguments apply to other classes of algebras assuming they have a Fraisse limit and satisfy the finite embeddability property.

Full work available at URL: https://arxiv.org/abs/0801.1212

zbMATH Keywords

latticeinterpolationembeddingpolynomialfinite latticesimpleorder-preserving functionlocally finite``typical property

Mathematics Subject Classification ID

Baire category, Baire spaces (54E52) Products, amalgamated products, and other kinds of limits and colimits (08B25) Partial algebras (08A55) Categoricity and completeness of theories (03C35)

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